Famous parents - Jones and Douglas

Talking about her worries for her child's future, she said: "In two years' time I want to be able to take my son to the park and not have to explain why 20 people with cameras are running after us.

"I hope the frenzy will die down so he won't have to sacrifice the good things just because photographers are documenting his every move."

In her latest film, Traffic, Zeta Jones stars alongside her husband as the pregnant wife of a drugs baron.

Her pregnancy was written into the plot after she confided her secret to director Stephen Spielberg when he offered her the role.

Media spotlight

The film, she said, opened her eyes to the dangers of drugs.

It also made her worry that being in the media spotlight could become too much of a strain for her son and that he might turn to drugs for help.

"He is the son of a famous mum, dad and grandfather," she explained.

His self-identity could be knocked constantly because he may have to work harder to make a name for himself as a lot of people will have the attitude `Oh he's from that family - everything is an easy ride for him'.

"Kids are at their most vulnerable when they are like that and it terrifies me."